Equilibrium curves are used in tire design to define the geometry of the tire particularly, e.g., the shape of the carcass, which is a reinforcing structure that extends through the crown or summit of the tire and between the bead regions located on each side of the tire. Upon the inflation and loading of the tire, the equilibrium curve used in designing and constructing the tire will substantially determine the stresses that will be experienced by belts in the summit. The equilibrium curve also helps determine the exterior profile of the tire as well as its potential for wear during use.
Conventionally, the equilibrium curves used for tire design and construction have typically used a three-ply membrane model that provides significant curvature for the tire along the summit region. The carcass is usually constructed to follow the shape of the equilibrium curve. Belts in the summit that are placed over, or radially outside of, the carcass adopt much of their shape and, therefore, curvature from the shape of the carcass.
As used herein, “droop” refers to the difference in position, along the radial direction, between the center (i.e. at the equatorial plane) of a belt in the summit and the edge of such belt. As the tire rolls through the contact patch (the portion of the tire in contact with the road), the tire flattens in the contact patch when under a load. Droop in a summit belt contributes to the amount of tension experienced by the belt as it flattens in the contact patch. Such belt tension provides a limitation on the overall width to which a tire can be designed and constructed. This width limitation is undesirable because in certain applications a wider tire can provide performance advantages. For example, for certain commercial truck tire applications, a wide tire can replace a pair of narrower tires and provide improvements in fuel efficiency.
Additionally, droop in a summit belt leads to differences in rolling radii. More specifically, the radii from the axis of rotation for a drooping summit belt will likely be different at various locations along the axial direction. This difference can, in turn, result in different average longitudinal stresses along the contact patch between the center and shoulder regions of the tread so as to provide undesirable differences in wear rate across the tread width. Also, less evenly distributed contact pressure between the tire and road surface can occur across the contact patch so as to further aggravate differences in wear rate across the tread width.
Accordingly, a tire and/or equilibrium curve for a tire that can be used to avoid or minimize droop would be useful. More specifically, an equilibrium curve that allows designing and constructing wider tires with improvements in performance would be beneficial. Such an equilibrium curve that can allow e.g., the use of wider summit belts and tread widths with improvements in tread wear would also be particularly useful.